SANKAMPAENG, Thailand—Thailand's army is trying to co-opt some of the populist policies pioneered by the country's billionaire former leader and set itself up as the rescuer for the battered economy.

Its success depends on whether Gen. Prayuth Chan-ocha, who took over in a coup on May 22, can sell villagers and small-town entrepreneurs his own package of big-spending projects before they run out of patience and challenge his power...